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Math Help - Calculus Help

  1. #1
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    Calculus Help

    I need help finding the second derivative and critical numbers of this function.

    f(x)=x^{2/3}(x-3)^{1/3}
    I get a first derivative of
    f'(x)=2/9x^{1/3}(x-3)^{1/3}+1/3x^{2/3}
    and a second derivative of
    f"(x)=(x-3)^{1/3}+{2/9}x^{1/3}
    but i dont think this is right because I cant find the critical numbers
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jjedlicka View Post
    I need help finding the second derivative and critical numbers of this function.

    f(x)=x^{2/3}(x-3)^{1/3}
    I get a first derivative of
    f'(x)=2/9x^{1/3}(x-3)^{1/3}+1/3x^{2/3}
    and a second derivative of
    f"(x)=(x-3)^{1/3}+{2/9}x^{1/3}
    but i dont think this is right because I cant find the critical numbers
    indeed, there are no critical points. however, you're derivatives are not correct. you need to use the power rule here. it seems you attempted to, but it was not properly executed.

    recall: \frac d{dx}f(x)g(x) = f'(x)g(x) + f(x)g'(x)
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